Steiner Loops Satisfying the Statement of Moufang's Theorem

2015/09/20 by Maria de Lourdes Merlini Giuliani, Giuliani, Maria de Lourdes Merlini, Giliard Souza dos Anjos +3
Mathematics · #Mathematics and Applications #math.GR #msc:20N05

paper · pdf · doi:10.48550/arxiv.1509.06364

arxiv created 2015/09/20 · arxiv updated 2015/09/23

Abstract

Andrew Rajah posed at the Loops'11 Conference in Trest, Czech Republic, the following conjecture: Is every variety of loops that satisfies Moufang's theorem contained in the variety of Moufang loops? This paper is motivated by that problem. We give a partial answer to this question and present two types of Steiner loops, one that satisfies Moufang's theorem and another that does not, and neither is Moufang loop.

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